= Quartic Hermitian matrix two-point function
{title2=$\langle M^i{}_jM^k{}_l\rangle_c$}
For $S=a\operatorname{tr}(M^2)/2+b\operatorname{tr}(M^4)/4$ with $a>0$, the <Wick theorem> gives
$$
\langle M^i{}_jM^k{}_l\rangle_c
=\frac1a\delta^i{}_l\delta^k{}_j-\frac b{a^3}\left(2N\delta^i{}_l\delta^k{}_j+\delta^i{}_j\delta^k{}_l\right)+O(b^2).
$$
There are eight adjacent external-attachment contractions with one free matrix-index sum and four opposite attachments with no free sum. The second tensor structure is needed at finite $N$; omitting it is an additional large-$N$ approximation, not merely restricting to <connected Feynman diagrams>.
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